Drag coefficient of flow around a sphere: Matching asymptotically the wide trend

An empirical relationship of drag coefficient of flow around a sphere is developed for the entire range of Particle Reynolds numbers reported in the literature from Stokes regime to the condition when turbulent boundary layer prevails. The relationship is obtained using an approach to match asymptotically the wide trend of drag coefficient. The matching approach, which relies on dividing the wide trend into smaller segments that can be combined into an overall relationship, employs regression techniques and thus warrants the best-fit accuracy results. The relationship is calibrated with experimental data available in the literature covering the entire range for Reynolds numbers up to ~ 10⁶. For Reynolds values greater than 10⁶, the relationship renders a drag coefficient of 0.2. The performance of the relationship is tested and compared with other suitable models found in the literature. This relationship is also transformed into an explicit expression for settling velocity calculations.